zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Generalized algebra within a nonextensive statistics. (English) Zbl 1125.82300
Summary: By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators: addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g. associativity, commutativity and existence of neutral elements. On the contrary, the distributivity law and the opposite element are no more universal within the generalized algebra.

82C03Foundations of time-dependent statistical mechanics
80A05Foundations of classical thermodynamics
Full Text: DOI arXiv
[1] Jancovici, B.; Manificat, G.; Pisani, C.: Coulomb systems seen as critical systems: finite-size effects in two dimensions. J. stat. Phys. 70, 3147 (1994) · Zbl 0839.76100
[2] Hayward, Sean A.: Phys. lett. A. 256, 347-350 (1999)
[3] Frolov, V. P.; Fursaev, D. V.; Zelnikov, A. I.: Phys. lett. B. 382, 220 (1996)
[4] Jund, P.; Kim, S. G.; Tsallis, C.: Phys. rev. B. 52, 50 (1995)
[5] Cannas, S. A.; Tamarit, F. A.: Phys. rev. B. 54, R12661 (1996)
[6] Antoni, M.; Ruffo, S.: Phys. rev. E. 52, 2361 (1995)
[7] Grigera, J. R.: Phys. lett. A. 217, 47 (1996)
[8] Dauxois, T.; Ruffo, S.; Arimondo, E.; Wilkens, M.: Lecture notes in physics. 602, 1-19 (2002)
[9] Latora, V.; Rapisarda, A.; Ruffo, S.: Prog. theor. Phys. suppl.. 139, 204 (2000)
[10] Abe, S.; Rajagopal, A. K.; Plastino, A.; Lotora, V.; Rapisarda, A.; Robledo, A.: Letters to the editor: revisiting disorder and Tsallis statistics. Science 300, 249-251 (2003)
[11] Tsallis, C.: J. stat. Phys.. 52, 479 (1988)
[12] Curado, E. M. F.; Tsallis, C.: J. phys. A: math. Gen.. 24, L69 (1991)
[13] Pennini, F.; Plastino, A. R.; Plastino, A.: Physica A. 258, 446 (1998) · Zbl 1010.81522
[14] Salinas, Silvio R. A.; Tsallis, C.: Brazilian J. Phys. (Special issue: nonadditive statistical mechanics and thermodynamics). 29 (1999)
[15] Wang, Q. A.: Incomplete statistics: nonextensive generalization of statistical mechanics. Chaos, solitons & fractals 12, 1431 (2001) · Zbl 1022.82001
[16] Wang, Q. A.: Nonextensive statistics and incomplete information. Euro. phys. J. B 26, 357 (2002)
[17] Wang, Q. A.: Correlated electrons and generalized statistics. Euro. phys. J. B 31, 75-79 (2003)
[18] Wang, Q. A.; Le Méhauté, A.: Extensive form of equilibrium nonextensive statistics. J. math. Phys. 43, 5079-5089 (2002) · Zbl 1060.82002
[19] Tsallis, C.: Quimica nova. 17, 468 (1994)
[20] Yamano, Takuya: Physica A. 305, 486 (2002) · Zbl 0993.94010
[21] Aguiar, C. E.; Kodama, T.: Physica A. 320, 371 (2003)
[22] Borges, E. P.: A possible deformed algebra and calculus inspired in nonextensive thermostatistics
[23] Kaniadakis, G.: Physica A. 296, 405 (2001) · Zbl 0972.82012
[24] Abe, S.: Phys. rev. E. 63, 061105 (2001)
[25] Wang, Q. A.; Nivanen, L.; Le Méhauté, A.; Pezeril, M.: On the generalized entropy pseudoadditivity for complex systems. J. phys. A 35, 7003 (2002) · Zbl 1040.82001
[26] Abe, S.: Phys. lett. A. 271, 74 (2000)
[27] Wang, Q. A.: Chaos, solitons & fractals. 14, 765 (2002)
[28] Wang, Q. A.: Measuring information growth in fractal phase space · Zbl 1122.82306
[29] Beardon, A. F.: An introduction to hyperbolic geometry. Ergodic theory, symbolic dynamics and hyperbolic spaces (1991) · Zbl 0755.30001
[30] Le Méhauté, A.; Nigmatullin, R.; Nivanen, L.: Flèches du temps et géométrie fractale. (1998) · Zbl 0906.58026
[31] Le Méhauté, A.; Nivanen, L.: Proceedings of SPIE. 4061, 180 (2000)